Finite-Length Scaling of Spatially Coupled LDPC Codes Under Window Decoding Over the BEC
arXiv:2003.04421 · doi:10.1109/TCOMM.2020.3010958
Abstract
We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.
arXiv commentPublished in IEEE Transactions on Communications (Early Access). This paper was presented in part at the IEEE Information Theory Workshop (ITW), Visby, Sweden, August 2019 (arXiv:1904.10410)
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